A box contains one red ball, one purple ball, and one blue ball. Two balls are drawn from the box. What is the probability of drawing two balls of different colors, if the selection is replaced?

Rationale

The probability of drawing two balls of different colors is 0.67.

When two balls are drawn with replacement, the total number of possible outcomes is 3 (red, purple, and blue) for each draw, resulting in 3 x 3 = 9 total combinations. The combinations that yield two different colors are: red-purple, red-blue, purple-red, purple-blue, blue-red, and blue-purple, totaling 6 favorable outcomes. Thus, the probability is 6 out of 9, which simplifies to 0.67.

A (0.33) YOUR ANSWER

This value represents the probability of drawing two balls of the same color, which occurs if both draws yield either red, purple, or blue. There are only 3 outcomes (red-red, purple-purple, blue-blue) out of a total of 9 combinations, leading to a probability of 3/9 or 0.33.

B (0.5) YOUR ANSWER

This option incorrectly suggests an equal likelihood for drawing different colored balls versus same colored balls. The actual breakdown of outcomes shows that there are 6 combinations for different colors and only 3 for the same color, thus the probability for same colors is 0.33 and different colors is 0.67, making 0.5 inaccurate.

C (0.67) CORRECT

This is the correct answer, representing the probability of drawing two balls of different colors. As explained, the 6 favorable combinations of different colors out of 9 total combinations yield a probability of 0.67.

D (1) YOUR ANSWER

This choice implies that all draws will result in two balls of different colors, which is impossible given that there is a chance for both draws to yield the same color. The existence of outcomes where the same color is drawn (3 combinations) confirms that the probability cannot be 1.

Conclusion

In this probability scenario, drawing two balls with replacement from a set of three different colors results in a 0.67 chance of obtaining two balls of different colors. The calculations show that while there are multiple outcomes, the favorable combinations significantly outweigh those leading to the same color, confirming the correctness of the answer.

A box contains one red ball, one purple ball, and one blue ball. Two balls are drawn from the box. What is the probability of drawing two balls of different colors, if the selection is replaced?

The probability of drawing two balls of different colors is 0.67.

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